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Combustion and Flame 150 (2007) 2–26www.elsevier.com/locate/combustflame

Feature Article

Detailed characterization of the dynamics ofthermoacoustic pulsations in a lean premixed swirl flame

W. Meier ∗, P. Weigand, X.R. Duan 1, R. Giezendanner-Thoben 2

Institut für Verbrennungstechnik, Deutsches Zentrum für Luft- und Raumfahrt (DLR), Pfaffenwaldring 38,D-70569 Stuttgart, Germany

Received 28 November 2006; received in revised form 2 April 2007; accepted 3 April 2007

Available online 23 May 2007

Abstract

A nozzle configuration for technically premixed gas turbine flames was operated with CH4 and air at at-mospheric pressure. The flames were confined by a combustion chamber with large quartz windows, allowingthe application of optical and laser diagnostics. In a distinct range of operating conditions the flames exhibitedstrong self-excited thermoacoustic pulsations at a frequency around 290 Hz. A flame with P = 25 kW thermalpower and an equivalence ratio of Φ = 0.7 was chosen as a target flame in order to analyze the dynamics andthe feedback mechanism of the periodic instability in detail. The velocity field was measured by three-componentlaser Doppler velocimetry, the flame structures were measured by chemiluminescence imaging and planar laser-induced fluorescence of OH, and the joint probability density functions of major species concentrations, mixturefraction, and temperature were measured by laser Raman scattering. All measuring techniques were applied in aphase-locked mode with respect to the phase angle of the periodic pulsation. In addition to the pulsating flame,a nonpulsating flame with increased fuel flow rate (P = 30 kW, Φ = 0.83) was studied for comparison. The mea-surements revealed significant differences between the structures of the pulsating and the nonpulsating (or “quiet”)flame. Effects of finite-rate chemistry and unmixedness were observed in both flames but were more pronouncedin the pulsating flame. The phase-locked measurements revealed large variations of all measured quantities duringan oscillation cycle. This yielded a clear picture of the sequence of events and allowed the feedback mechanism ofthe instability to be identified and described quantitatively. The data set presents a very good basis for the verifi-cation of numerical combustion simulations because the boundary conditions of the experiment were well-definedand the most important quantities were measured with a high accuracy.© 2007 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Gas turbine combustion; Combustion oscillation; Swirl flame; Turbulence–chemistry interaction; Validationmeasurements

* Corresponding author. Fax: +49 711 6862 578.E-mail address: [email protected] (W. Meier).

1 Current address: Southwestern Institute of Physics, P.O. Box 432, 610041 Chengdu Sichuan, People’s Republic of China.2 Current address: Robert Bosch GmbH, Postfach 10 60 50, 70049 Stuttgart, Germany.

0010-2180/$ – see front matter © 2007 The Combustion Institute. Published by Elsevier Inc. All rights reserved.doi:10.1016/j.combustflame.2007.04.002

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W. Meier et al. / Combustion and Flame 150 (2007) 2–26 3

1. Introduction

In stationary gas turbines (GT) the concept oflean premixed combustion is widely used in orderto meet the stringent demands for low emissions ofNOx . This concept also allows the achievement ofa quite homogeneous temperature distribution at theturbine inlet and thus a lower thermal load. Unfor-tunately, lean premixed GT flames are susceptible tothermoacoustic instabilities driven by the combustionprocess and sustained by a resonant feedback mecha-nism coupling pressure and heat release [1–7]. Thesepulsations can lead to strong perturbations in the gasturbine and even to the destruction of system compo-nents. The physical and chemical mechanisms drivingthe instabilities are based on a complex interaction be-tween combustor geometry, pressure, flow field, mix-ing, chemical reactions, and heat release and are notunderstood well enough yet. While active and passivecontrol mechanisms have been developed to reduceor even eliminate instabilities in some industrial burn-ers [8–12], the problem is not fundamentally solved.Major efforts are currently being made in the devel-opment of numerical simulation tools in order to pre-dict unsteady combustion behavior so that improvedGT combustors can be designed with their help [1–3,13–17]. However, a deeper understanding of the com-plex interactions involved in combustion instabilitiesis now and in the near future based on experimentalresearch using advanced measuring techniques withhigh temporal and spatial resolution.

In order to investigate the phenomenon of com-bustion pulsations, the German Aerospace Center(DLR) has performed comprehensive measurementsin an atmospheric pressure GT model combustor. Thecombustor was operated with premixed CH4/air andexhibited a self-excited thermoacoustic instability.The burner nozzle was designed by Turbomeca S.A.[18,19]. In this configuration CH4 was mixed into theair flow within the radial swirler of the nozzle [18].The flames were confined by a combustion chamberwith an exhaust tube at the top. The flame investigated(equivalence ratio of Φ = 0.7, thermal power 25 kW)exhibited a strong self-excited thermoacoustic oscilla-tion at a frequency of about 290 Hz. For comparison,a nonpulsating (or “quiet”) flame with Φ = 0.83 andthermal power 30 kW was also measured. The maingoals of the investigations were a deeper understand-ing of the physical and chemical mechanisms drivingthe oscillation and the provision of a database ofexperimental results which shall be used for the com-parison with numerical simulations. For the validationpurposes, great care was taken to specify the experi-mental uncertainties and to characterize the boundaryconditions.

The combustion chamber was equipped with largequartz windows in order to apply laser and opticaldiagnostic techniques. The measurements were per-formed with phase resolution, i.e., triggered with re-spect to the phase of the pressure pulsation measuredby a microphone. The shape and position of the flamezone were determined by OH chemiluminescencemeasurements. These measurements also yielded ameasure of the heat release rate [20,21]. The flowvelocities were measured by LDV and the joint prob-ability density functions of major species concen-trations, temperature, and mixture fraction by laserRaman scattering. Due to its ability of multispeciesdetection, the single-shot Raman technique is of spe-cial value for the flame investigation because it yieldsinformation about mixing and finite-rate chemistry ef-fects [22,23]. Previous investigations in nonpremixedand partially premixed swirl flames demonstrated thatturbulence–chemistry interactions play an importantrole in those flames [24–26]. Furthermore, Ramanmeasurements characterize the mixing process, e.g.,mixing of burnt gas from the recirculation zones withfresh gas from the nozzle, which represents the mainstabilization mechanism in strongly swirling flames.Another important parameter is the degree of un-mixedness in industrial-type premixed flames, as thiscan have a significant influence on flame stabilizationand NO formation [27]. It is also known that equiva-lence ratio fluctuations can be the source of combustorinstabilities [28–32]. Thus, the measurement of thegas composition is of great importance for this inves-tigation.

In previous experiments at the DLR, another GTburner was employed to study the details of thermoa-coustic instabilities using the same optical combus-tion chamber and the same measuring techniques [33,34]. In that study, periodic variations of the mixing ofexhaust gas from the recirculation zones with freshgas were identified as the main source of the peri-odic changes of the heat release rate. In the burnerexamined in the present study, the feedback mech-anism is of a different nature. In the current paperthe combustor configuration is presented and resultsfrom phase-resolved measurements of OH* chemilu-minescence, flow velocities, mixture fraction, temper-ature, and species concentrations are shown. Effectsof mixing and turbulence–chemistry interactions areaddressed and periodic variations of the gas flow ratesat the inlet of the combustion chamber are discussed.

2. Combustor and target flames

The gas turbine model combustor was derivedfrom an industrial design by Turbomeca. In Fig. 1a schematic of the nozzle design with the combus-

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4 W. Meier et al. / Combustion and Flame 150 (2007) 2–26

Fig. 1. Schematic of the injector with combustion chamberand photo of the flame.

tion chamber is shown. Dry air at ambient temper-ature is fed via a plenum (� = 78 mm) through 12radial swirler vanes to the burner nozzle. The fuel gas(CH4) is injected into the air flow through small holes(� = 1 mm) within the radial swirler with high mo-mentum to ensure good mixing before it enters thecombustion chamber. The nozzle exit has a diame-ter of 27.85 mm. The air and fuel flows were eachmeasured by two different mass-flow meters (BrooksType 5853S for air and 5851S for CH4 and DanfossType 2100). The accuracy of the flow measurementswas ±1.5%. The exit plane of the nozzle was definedas h = 0 for all measurements.

The combustion chamber consists of large quartzwindows of thickness 1.5 mm held by steel posts inthe corners, thus creating a confinement with a square

section of 85 × 85 mm and a height of h = 114 mm.The exit of the upright combustion chamber is cone-shaped, leading to a short central exhaust pipe witha diameter of 40 mm. The large windows on eachside enable unobstructed optical access to nearly thewhole flame zone and in particular close to the nozzleexit. In order to change the measuring location withinthe flames, the burner could be translated in axial andradial directions. The burner position was measuredby photoelectric encoder systems. The measuring ac-curacy for the distance between the radial and axialmeasuring locations was estimated to be ±0.1 mmand the day-to-day reproducibility to be ±0.5 mm.

Two different flames were investigated: (1) An un-steady, pulsating flame operated at 25 kW with anequivalence ratio of Φ = 0.70 that exhibited thermoa-coustic pulsations at a frequency of f ≈ 290 Hz. Forthese operating conditions the Reynolds number atthe exit of the nozzle, based on the cold flow and theexit diameter, is about 35,000 and the swirl number,derived from the velocity measurements at 1.5 mmabove the exit, is approx. 0.6. (2a) A quiet flame with30 kW and Φ = 0.83 (for the LDV measurementsthe flame was operated under slightly different con-ditions, i.e., 27 kW and Φ = 0.75, termed 2b). Theflame parameters are summarized in Table 1. The Kol-mogorov length scale was estimated to be on the orderof 0.1 mm in the turbulent flame regions; the corre-sponding time scale is 35 µs.

After a warm-up period of typically 30 min, thecombustor would reach a constant temperature. Con-tact of the fuel/air mixtures with the higher tempera-ture plenum and nozzle resulted in a slight preheating.The fuel/air mixtures were measured to reach temper-atures between T ≈ 320 and 380 K prior to enteringthe combustion chamber. The pressure drop betweenthe plenum and the combustion chamber was on theorder of 8–9 mbar.

Whereas the LDV measurements were performedat the DLR research facility in Berlin, the Raman,LIF, and chemiluminescence measurements were per-formed at the DLR facility in Stuttgart. The measure-ment campaigns were performed on different days,and the phase-resolved Raman measurements wereperformed over several days. The ambient pressure

Table 1Investigated flames

Air CH4 Pth Φ f Tad(295 K)

sl/min g/min sl/min g/min (kW) (K)

1 570 734.2 41.8 30 25.1 0.70 0.0391 18342a 570 734.2 50.0 35.9 30.0 0.83 0.0463 20372b 570 734.2 45.0 32.3 27.0 0.75 0.0418 1915

Note. sl/min means standard liters per minute (standard conditions are 0 ◦C and 1013 mbar). f is mixture fraction correspondingto the equivalence ratio. Adiabatic flame temperature Tad was calculated for a fresh gas temperature of 295 K.

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Fig. 2. Pressure signals and respective spectra from the plenum and the combustion chamber.

was 995 to 1030 mbar during the LDV measurementsand 955 to 985 mbar during the Raman measure-ments. Because the air and fuel mass flows were keptconstant (as stated in the table), the difference in am-bient pressure resulted in a difference in flow velocityand density. It should be kept in mind that this mighthave a small influence on the flame behavior.

3. Pressure pulsations and phase angleassignment

The pressure fluctuations were measured with twomicrophone probes (Brüel & Kjær 4939—1/4′′), onemounted flush with the inner wall of the plenum andthe other connected to an air-cooled probe in one ofthe posts of the combustion chamber at the positionsshown in Fig. 1. The pressure signals from the plenumand from the combustion chamber and their respectivepower density spectra are shown in Fig. 2. The figureshows that the trace of the signal from the plenumis smoother than that from the combustion chamber.As the frequency peaks in both spectra are very pro-nounced and no shift of the frequency occurs betweenthe two positions, the signal from the plenum wastaken as the reference for triggering the phase-lockedmeasurements. The microphone signal was of suffi-cient magnitude and clarity that no filtering was nec-essary for accurate triggering. The maximum ampli-tude of the acoustic pressure in the combustion cham-

ber was determined to be on the order of 1.2 mbar.The acoustic pressure in the plenum was higher bya factor of about 1.4. The measurements further re-vealed that the pressure variation in the combustionchamber ran ahead of the pressure variation in theplenum by approximately 80◦. Under the conditionsprevailing in the plenum, f ≈ 290 Hz corresponds toa wavelength of λ ≈ 1.2 m; under the conditions inthe combustion chamber to λ ≈ 2.8 m. These wave-lengths are large compared to the dimensions of theplenum and combustion chamber and the phase dif-ferences within the plenum or combustion chamberare on the order of 10◦–15◦.

In order to adapt the repetition rate of the ICCD-camera system (≈1 Hz) and the pulsed laser systemsfor Raman (≈5 Hz) and LIF (≈10 Hz) to the oscilla-tion frequency of the flame (f ≈ 290 Hz), a triggeringscheme with inhibition times was set up as follows.The negative-to-positive transition of the microphonesignal from the plenum triggered a delay generator(SRS, DG535), which itself generated the trigger sig-nal for the laser or the camera systems after a timedelay dt1. The inhibition time dt1 was adjusted ac-cording to the repetition rate of the laser and camerasystems. After the inhibition time had passed, the nextnegative-to-positive transition of the microphone sig-nal initiated the trigger sequence. In order to carryout the measurements at different phase angles, a de-lay time dt2 (= 0 to 1/f ) was applied as indicated inFig. 3 [33]. The delay time dt2 (� 1/f ≈ 3.4 ms) was

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Fig. 3. Pressure signal of the plenum with trigger scheme forthe pulsed measurements.

Fig. 4. Pressure oscillation compared to a pure sine func-tion; the black curve shows a sine function and the redcurve displays the pressure signal of the plenum. Themarkers ph1–ph8 indicate the assigned phase angles atwhich measurements were performed. These were ph1 = 0◦ ,ph2 = 50◦ , ph3 = 105◦ , ph4 = 150◦ , ph5 = 195◦ , ph6 =230◦ , ph7 = 270◦ , and ph8 = 315◦ .

small compared to dt1 (≈100 ms) and thus permittedstable operation of the laser system.

Measurements were performed at eight phase an-gles. The assignment of the phase angles was chosentaking the minimum, maximum, and medium pres-sure values as reference points ph1, ph3, ph5, andph7, respectively. The additional phase angles, ph2 toph8, were taken in the (temporal) middle between ad-jacent phase angles. It should be noted the pressuresignal was not perfectly sinusoidal. The phase trig-gering and the pressure trace are shown in Fig. 4 incomparison to a pure sine wave. It can be seen that thepressure rise (maximum at 195◦) was slightly slowerthan the pressure drop. Due to a permanently presentjitter of the frequency on the scale of approx. ±5 Hz(±1.7%), the reference points also jittered by ±1.7%,resulting in a corresponding uncertainty of the phase

assignment. The minimum pressure in the plenumwas arbitrarily assigned as ph1 = 0◦. Accordingly, theminimum pressure in the combustion chamber was at−80◦ or 280◦, close to ph7.

4. Measuring techniques

4.1. Laser Doppler velocimetry

The three velocity components were measured si-multaneously by LDV using an Ar+-laser (Coherent,Innova 90) and two orthogonally positioned Dantec-DISA optics (DISA 55X and DISA flow directionadapter). Commercial camera lenses were used to fo-cus the signals in forward scattering onto three pho-tomultiplier tubes. Signal recording and pretreatmentwere performed with Dantec BSA enhanced units(57N20 + 57N35). The seeding particles (TiO2, d ≈0.8 µm) added to the air flow were small enough tofollow the large-scale turbulence up to >1 kHz [35].In order to link the velocity signals to the pressurefluctuations, the BSA units additionally recorded trig-ger events that were created by the positive zero cross-ing of the pressure signal from the plenum. In a post-processing step, the velocity signals were assortedaccording to their arrival times into 72 phases (stepsof 5◦) each covering a 10◦ window (±5◦). The mea-surements were performed in one vertical plane alongradial profiles at the heights h = 1.5, 5, 15, 25, and35 mm in order to capture the flow field, especially atthe nozzle exit. The radial spacing was �r = 1 mmat h = 1.5 mm and 2 mm at the other heights. Ateach position 100,000–200,000 velocity data wererecorded. The resulting probe volumes were about60 µm in diameter and 1.0 mm in length for axial(u) and radial (v) velocity components and 120 µmand 1.5 mm for the tangential (w) direction of thevelocity. The sorted velocity data were selected ac-cording to the phase assignment (ph1–ph8) explainedabove (Fig. 4). The uncertainty of the velocity mea-surements for each phase is typically 1.5–2% for themean value and 2–2.5% for the rms value.

4.2. OH* chemiluminescence detection

OH* chemiluminescence was imaged using an in-tensified CCD camera (Roper Scientific) equippedwith an achromatic UV lens (f = 100 mm, f/2, HalleNachf.) and an interference filter with high transmis-sion between 295 and 342 nm (Laser ComponentsGmbH). The plane of focus of the system was locatedat the center of the combustion chamber. Althoughimage sharpness decreased with increasing distancefrom this plane, lines separated by 1 mm could stillbe resolved at the forward and rear windows of the

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chamber. Sets of 100 images (exposure time 130 µs)were accumulated at each of the eight phase anglesoutlined above. OH* chemiluminescence intensitiesfrom lean premixed flames represent an indicator forthe heat release rate [20,21], but the correlation be-tween OH* chemiluminescence and heat release ratemay be influenced by multiple parameters and is stillsubject to research [6,36]. Thus from these imagesonly qualitative information can be deduced about thephase-dependent variations in heat release and the lo-cation and extension of the flame zone. Even thoughthis technique is line-of-sight integrated, spatially re-solved information can be gained by deconvolution,taking advantage of the rotational symmetry of theflame. This results in a quasi 2-D image of the centerplane where the local distribution of the chemilumi-nescence can be identified more clearly than in theintegral view.

4.3. Planar laser-induced fluorescence of OH

PLIF of OH radicals was applied to visualize theflame structures. A pulsed Nd:YAG-pumped dye laserwas used to supply pulsed laser radiation for the exci-tation of OH on the R2(13) line of the A2Σ+–X2Π

(ν′ = 1, ν′′ = 0) transition at λ = 282.6 nm. Thebeam was formed to a vertical sheet (h ≈ 55 mm) anddirected into the combustion chamber intersecting theflame axis. The pulse energies at the measuring loca-tion were typically 1.5 mJ/pulse with a band widthof about 0.45 cm−1 and a duration of 5 ns. The sheetthickness was approximately 0.8 mm in the imagedarea. The resulting spectral laser intensities were onthe order of 1.5 MW/cm2 cm−1. Considering thatthe saturation intensity is around 1 MW/cm2 cm−1,the applied laser intensities may have resulted in asmall degree of saturation (which is mostly unimpor-tant for the structural information gained from thePLIF images). The excited fluorescence signal wascollected at 90◦ by an achromatic UV lens (f =100 mm, f/2, Halle Nachf.) equipped with an in-terference filter (λ ≈ 295–342 nm) and detected byan intensified CCD camera (LaVision Flamestar II,286 × 384 pixels). The temporal detection gate of theimage intensifier was 50 ns. The spatial resolution ofthe measurement is mainly limited by the thickness ofthe laser sheet (0.8 mm). In the other two directions,i.e., in the image plane, the spatial resolution is on theorder of 0.3 mm.

4.4. Laser Raman scattering

For the pointwise quantitative measurement of themajor species concentrations (O2, N2, CH4, H2, CO,CO2, H2O) and the temperature, laser Raman scatter-ing was applied [37]. The radiation of a flashlamp-

pumped dye laser (Candela LFDL 20, wavelengthλ = 489 nm, pulse energy Ep ≈ 3 J, pulse durationτp ≈ 3 µs) was focused into the combustion chamberand the Raman scattering emitted from the measur-ing volume (length ≈ 0.6 mm, diameter ≈ 0.6 mm)was collected by an achromatic lens (D = 80 mm,f = 160 mm) and relayed to the entrance slit of aspectrograph (SPEX 1802, f = 1 m, slit width 2 mm,dispersion ≈ 0.5 nm/mm). The dispersed and spa-tially separated signals from the different specieswere detected by individual photomultiplier tubes(PMTs) in the focal plane of the spectrograph andsampled using boxcar integrators. The species num-ber densities were calculated from these signals usingcalibration measurements and the temperature wasdeduced from the total number density via the idealgas law [37]. The simultaneous detection of all majorspecies with each laser pulse also enabled the deter-mination of the instantaneous mixture fraction [38].In the data sets the mixture fraction defined by Bilger[39,40] is used.

Due to restrictions of the optical access of the Ra-man setup, measurements could not be performed forh < 6 mm and r > 30 mm. In the pulsating flame,phase-resolved measurements were performed at h =6, 15, 25, 35, and 60 mm over a scan pattern of 50points altogether. The radial spacing was �r = 2 mmat h = 6 mm, �r = 3 mm at h = 15 mm, �r = 4 mmat h = 25 and 35 mm, and �r = 5 mm or 10 mmat h = 60 mm. At each point in the scan pattern 400single-shot measurements were acquired. These datawere used to compute joint probability density func-tions (PDF). At some locations, where turbulent orphase-dependent fluctuations were very small (espe-cially in the outer region of the flame), less than 400samples were recorded. In the pulsating flame, Ramanmeasurements were also performed without phase-locking; i.e., the measuring system was triggered atrandom phase angle. In this case, measurements wereperformed at h = 6, 10, 15, 20, 30, 40, 60, and 80 mm,and 500 single-shots were taken at each location. Inthe quiet flame Raman measurements were performedat h = 6, 10, 15, 20, 30, 40, 60, and 80 mm (500 shotsat each location).

Signal interferences from C2 and PAHs were verylow in the flames investigated and there was littleneed for correction procedures. Nonetheless, the sig-nal background was recorded by additional PMTs inRaman-free spectral regions and the few samples withsignificant background were filtered out in the data re-duction routine. Single-shot measurements with PMTsaturation or unrealistic C/H or N/O ratios were alsodiscarded during data evaluation. Thus, the final datasets do not always contain 400 (or 500) single-shotrealizations. For the phase-resolved measurements inthe pulsating flame the percentage of discarded sam-

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Table 2Summary of the measurement uncertainties (for details see text)

Measured quantity Systematic uncertainty Statistical uncertainty

Measuring location �h, relative ±0.1 mmMeasuring location �h, absolute ±0.5 mmMeasuring location �r , relative ±0.1 mmMeasuring location �r , absolute ±0.5 mmVelocity <0.5% ±1.5–2%Temperature ±3–4% ±2.5%Mixture fraction ±3–4% ±1%H2O mole fraction ±3–5% ±3% (density-dependent)O2 mole fraction ±3–5% ±7% (density-dependent)CO2 mole fraction ±3–5% ±7% (density-dependent)CO mole fraction ±5–10% ±20–50% (density-dependent)H2 mole fraction ±5–10% ±10–30% (density-dependent)CH4 mole fraction +5–9% ±1–3% (density-dependent)

ples was 3.5% in the worst case (at h = 6 mm, r =10 mm) and on average it was below 0.6%. For themeasurements without phase resolution in the pulsat-ing flame, the percentage of discarded samples was4.8% in the worst case (at h = 6 mm, r = 6 mm)and on average it was below 1.2%. For the measure-ments in the stable flame the worst case was 4.4%(h = 6 mm, r = 10 mm) and the average percentageof discarded samples was smaller than 0.7%. A sig-nificant bias of the joint PDFs due to filtering wasnot observed. For example, in the worst case in thepulsating flame, the mean values of T , f , and themole fractions of the major species changed by lessthan 0.5% due to filtering.

With respect to measurement uncertainties, onemust distinguish between systematic errors arisingfrom, for example, uncertainties in the calibrationprocedure and statistical errors that are mainly causedby the statistics (shot noise) of the detected Ramanphotons NP in a single-shot measurement. System-atic uncertainties were typically ±3–4% for the tem-perature and mixture fraction, ±3–5% for the molefractions of O2, H2O, and CO2, and ±5–10% forH2 and CO. The systematic errors are largely inde-pendent of the mole fraction and temperature in theflame. In the measurements reported here, it turnedout that the evaluated CH4 mole fractions were sys-tematically too large by about 7%. In regions withsignificant amounts of CH4 the measured mixturefraction was therefore also biased to larger values (upto ≈7%). The statistical uncertainties were quantifiedby recording single-shot data sets in stable laminarflames. The rms fluctuations in these flames were, forexample, 2.5% for T at T = 1916 K, 3.2% for H2Oat a mole fraction of X(H2O) = 0.19, 7% for O2 atX(O2) = 0.06, 7.4% for CO2 at X(CO2) = 0.068,and 1% for the mixture fraction. In an electricallyheated flow of pure CH4 the rms value was 1% at850 K. To a good approximation the rms fluctuations

scale with N−0.5P . Due to this dependence, the sta-

tistical uncertainties are quite large for CO and H2.The cross talk correction for CO leads to an additionalerror source, so that the statistical error for CO is 20–50%. The uncertainties are summarized in Table 2.The statistical uncertainty due to shot noise of de-tected signal photons is only relevant for single-shotmeasurements. For the mean value from a PDF com-prising 500 single-shot measurements, shot noise isnegligible because the number of signal photons forthe complete PDF is 500 · NP. Systematic and sta-tistical uncertainties are largely independent of eachother.

A further uncertainty concerns the number ofsingle-shot measurements necessary to reproduce thetrue PDF. This question cannot be answered in gen-eral because the necessary number of samples de-pends on the shape of the true PDF. To estimate theuncertainty a measured PDF can be used, and theconvergence of, e.g., the mean value with the num-ber of samples can be considered. It turned out thatin regions with strong turbulent fluctuations the finalmean value is typically reached to within 2% after300 samples. A number of 400 to 500 single shotsat each location thus seems a good trade-off betweenmeasuring time and convergence.

5. Results

5.1. Time-averaged velocity distributions

Fig. 5 shows plots of the combined mean u andv velocity components of the pulsating and quietflames. For most of the measuring heights in the pul-sating flame, data were taken only on one side of theflame axis, because of the assumption of axial sym-metry. In Fig. 5 the profiles in the upper panel (pul-sating flame) are mirrored to yield a better impression

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Fig. 5. Vector plot of combined mean u and v velocity com-ponents of the pulsating and the quiet flame. Negative veloc-ities are displayed in red.

of the flow field. Three different flow regions can bedistinguished: (1) The inlet flow of fresh gases whichis conically shaped; (2) an inner recirculation zone(irz); and (3) an outer recirculation zone (orz). It isseen that the inflow of the quiet flame is more widelyopened and exhibits a broader irz in comparison to thepulsating flame. Slight deviations from axial symme-try are seen in the profiles of the quiet flame withinthe irz. Similar deviations can be found in the pro-files of the other velocity components and of the rmsfluctuations. These deviations are not explained bythe measurement uncertainty and are probably real.However, the effects are small and are neglected inthe further discussion. The velocities of the reverseflow are higher in the pulsating than in the quietflame. This can be seen more clearly in the radial pro-files of Fig. 6, displaying the mean axial velocities ath = 1.5 mm. The irz of the pulsating flame extendsto r ≈ 4 mm at this height and reaches a mean axialvelocity of u ≈ −24 m/s. The quiet flame has nega-tive axial velocities of up to u ≈ −10 m/s and its irzextends to r ≈ 6 mm at h = 1.5 mm. The mean ax-ial velocity of the inflow is on the order of 35 m/sfor both flames, but the radial region of the inflow isbroader for the pulsating flame. The outer recircula-tion zones are characterized by very low axial veloci-ties and radial velocities that are directed to the flameaxis.

From Figs. 5 and 6 it is clear the mean flowfields of the two flames exhibit significant differences.However, it should be kept in mind that the pulsating

Fig. 6. Radial profiles of the mean axial velocity of the pul-sating and the quiet flame at h = 1.5 mm.

flame is subject not only to turbulent fluctuations butalso to periodic variations of the flow field. This willbe considered in the following section.

5.2. Phase-resolved velocity distributions

The phase-dependent variations of the mean axial,radial, and tangential velocity components are dis-played in Fig. 7 for the heights h = 1.5, 5, 25, and35 mm. It is clearly seen that the flowfield variesdrastically during an oscillation cycle. The profilesof umean near the nozzle (h = 1.5 and 5 mm) showthat the irz changes strongly in radial expansion andvelocity with a maximum expansion around ph5 anda minimum expansion around ph1. Accordingly, theradial extension of the inflow varies between �r ≈9 mm (ph5–ph7) to �r ≈ 14 mm (ph2). In the outerradial region the axial velocities are very small. Ath = 5 mm the variations of umean are still promi-nent and at h = 25 mm they have become relativelysmall but at h = 35 mm differences again become ap-parent. The radial velocity component is significantlysmaller than the axial component and the periodicvariations of vmean are not generally in phase withumean. At h = 1.5 and 5 mm, vmean is positive (i.e.,directed outward) out to r ≈ 15 mm and r ≈ 17 mm,respectively, and becomes negative further outside.The negative values of vmean characterize the outerrecirculation zone. In contrast to umean, the variationsof vmean become stronger further downstream, as canbe seen in the radial profiles at h = 25 and 35 mm.At h = 25 mm the injected gases are rapidly movingoutward at around ph2 (vmean > 25 m/s), but vmeanbecomes rather small around ph7. At 10 mm furtherdownstream (h = 35 mm) the flowfield looks quitedifferent: now vmean is very small at ph2 and the max-imum occurs at ph4. Considering the variation of theflowfield near the nozzle, the fast radial movement ath = 25 mm is associated with a broad inflow and vice

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Fig. 7. Phase-resolved radial velocity profiles of mean axial (u), radial (v), and tangential (w) velocity components at h = 1.5,5, 25, and 35 mm. Note the different scales at the axis.

versa. The tangential velocity component w exhibitssignificant phase-dependent variations for all measur-ing heights. At h = 1.5 mm maximum values around35 m/s and steep gradients of wmean are observed.With increasing height the profiles flatten and be-come broader. At h = 35 mm the maximum wmean isaround 12 m/s. Near the nozzle (h = 1.5 and 5 mm),wmean and umean are quite well in phase with respectto radial extension and amplitude; however, wmean isquite low in the irz, independent of phase angle. Theprofiles of wmean reflect neither a solid body rotationnear the axis (where w would linearly increase with r)nor a potential vortex further outside (where w woulddecrease as 1/r).

The pumping motion of the flowfield is of courserelated to the pressure variations in the combustionchamber and the plenum. However, the details of thisrelationship depend on the geometry of the nozzle, theacoustic behavior of the configuration, and the tem-perature distribution. In a very simplified approach,assuming the inflow is influenced only by the pres-sure variation in the combustion chamber (pchamber)and that the pressure has a sinusoidal temporal vari-ation, the axial velocity of the inflow would behaveaccording to du/dt ∼ −pchamber. In this simplifiedapproach one would expect the velocity to reach itsmaximum 90◦ after the pressure minimum in thecombustion chamber. The pressure minimum in the

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Fig. 8. Imaged chemiluminescence intensity distribution at eight different phase angles. Each image was averaged over 100 shotswith an exposure time of 130 µs each. Scales are in mm.

combustion chamber is around ph7 (−80◦ or 260◦)and from the simplified approach one would then ex-pect high inflow velocities in the nozzle around ph1,which is in qualitative agreement with the measure-ment. Naturally, the real situation is much more com-plex, but a quantitative analysis is beyond the scopeof this work.

5.3. Phase-resolved OH* chemiluminescence

Fig. 8 shows the mean OH* chemiluminescencefield measured at each of the eight phase angles stud-ied. Each field represents the ensemble average of 100images and each image was acquired with a 130-µsexposure time. Fig. 8 clearly shows that the intensity

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Fig. 9. Fig. 9: Normalized integrated OH chemilumines-cence and normalized pressure variation in the combustionchamber.

varies significantly during an oscillation cycle, with amaximum close to ph3 and a minimum half a periodlater. The chemiluminescence distributions resemble,of course, the photo of the flame in Fig. 1. The darkregions near the nozzle are associated with the inflowof the fresh gases, but include also the orz. It can fur-ther be seen that combustion is already taking placeat h = 0 for all phase angles and that the flame rootextends to h < 0. At ph1 to ph4 the main region ofheat release is at h ≈ 40–60 mm and r � 20 mm. Inthese images it has to be considered that the chemilu-minescence is integrated along the line of sight. Moredetails of the structure will be discussed on the basisof the deconvoluted images below.

The OH* chemiluminescence intensity integratedover the imaged area is displayed in Fig. 9 as a func-tion of phase angle together with the pressure vari-ation in the combustion chamber. It is seen that theintegrated chemiluminescence varies between 16 and100% and that this variation is quite well in phasewith the pressure variations. Provided the integratedchemiluminescence represents the total heat releaserate, the result demonstrates that the Rayleigh crite-rion for self-sustained combustion pulsations is ful-filled.

The deconvoluted chemiluminescence distribu-tions corresponding to the images in Fig. 8 are dis-played in Fig. 10. These represent quasi-2D cutsthrough the flame provided that cylindrical symme-try is present. Here, the phase-dependent changes ofthe flame shape can be seen more clearly. The flame isanchored near the central bluff body at h � 0 mm andfor lower heights (h < 30 mm) combustion is onlytaking place in the central region where r < 20 mm.At the base of the flame the chemiluminescence in-tensity is highest around ph1–ph3, when the reverseflow increases strongly. Throughout most of the os-cillation cycle the flame is hitting the wall (located atr = 42.5 mm) further downstream at h ≈ 30–70 mm.

It should be noted that the very high intensities at thewall and also the large gradients are an artifact of theAbel inversion routine [41]. Due to the sharp cutoff atthe wall, the gradient is overestimated by the program.However, for ph2–ph4, there are high chemilumines-cence intensities at h ≈ 40–60 mm that represent thelargest contribution to the integrated chemilumines-cence (see Fig. 9).

5.4. Phase-resolved OH PLIF distributions

Fig. 11 shows examples of single-shot OH PLIFimages recorded in the pulsating flame at four dif-ferent phase angles. Before the results are discussed,a few explanations about OH concentrations in flamesshould be given. At chemical equilibrium, the OHconcentration increases exponentially with temper-ature. The increase is, however, different for fuel-lean and fuel-rich mixtures [42]. In fuel-lean mix-tures, OH concentrations are detectable above T ≈1400–1500 K, while in fuel-rich mixtures, the OHequilibrium concentrations are significantly lower andbarely detectable by LIF below 1900 K. However,in reaction zones, OH is formed in superequilibriumconcentrations, which in turbulent flames are typi-cally several times higher than at equilibrium. Thelifetime of this superequilibrium OH is several mil-liseconds at atmospheric pressure. Thus, the highestOH concentrations within a PLIF image stem proba-bly from superequilibrium OH, i.e., “young” OH thathas just been formed in a reaction zone. Medium OHconcentration levels are typical of high-temperatureregions with “old” OH at chemical equilibrium. TheR2(13) line was used for excitation because two-lineOH PLIF thermometry measurements were also con-ducted within this experiment (not reported here). Thesecond excitation line for those measurements was theP1(2) line [43]. For the R2(13) line the Boltzmannfraction fB of the initial state changes significantlywith T ; for example, it increases by about 72% be-tween 1500 and 2200 K. However, the quenchingrate also increases with T , and a calculation usingLASKIN [44] showed that the fluorescence quan-tum efficiency QE decreases by ≈37% from 1500to 2200 K for an exhaust gas composition from sto-ichiometric combustion. Without taking variations ofthe gas composition into account, the net effect fromchanges in fB and QE yields a variation of about 30%over the temperature range considered. Within thislimit, the displayed OH LIF signals are representativeof the OH density.

The single-shot images in Fig. 11 are dominatedby turbulent fluctuations and do not well reflect thephase-dependent variations which are identified in theensemble-average images (discussed below). In theimage recorded at ph1, the region around the flame

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Fig. 10. Abel-transformed OH chemiluminescence images corresponding to the distribution of Fig. 8.

axis shows medium OH LIF intensities (blue color)which most probably reflect “old” OH at rather hightemperatures. On each side of this region there arehigh OH LIF intensities (yellow and red) from h = 0to 20 mm. These stem presumably from “young” OH,i.e., from reaction zones and burnt gases next to the re-action zones. The low intensity regions farther outside

(black) have to be interpreted as fresh gas or mix-tures of fresh gas with some exhaust gas at temper-atures below 1400 K. In the outer recirculation zonesthe LIF intensities are quite low (violet) probably re-flecting “old” OH at intermediate temperatures. TheOH LIF distribution and the interpretation given areconsistent with the deconvoluted chemiluminescence

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Fig. 11. Examples of single-shot OH PLIF images at four different phase angles. Scales at axes are in mm; color bar is given inarbitrary units.

images displayed in Fig. 10, which show a flame re-gion in the area where high OH LIF intensities arepresent. The single-shot image at ph5 shows high OHLIF intensities on the flame axis, again in agreementwith the deconvoluted chemiluminescence image. Atph7, the OH LIF distribution shows quite nicely theinflow of the fresh gases (dark area). Considering thestructures within the single-shot samples, one can seethe wrinkled and convoluted boundary layer betweenthe different regions of the flow field, for example be-tween the irz and the inflow of fresh gases.

The ensemble averaged OH PLIF distributions arepresented in Fig. 12 for the eight phase angles stud-ied. It is seen that the highest mean OH LIF intensitiesare found in the irz, especially below h ≈ 30 mm,and that this region is surrounded by a low-intensitylayer, indicative of the inflow of fresh gases. Also,at ph3 and ph4, high intensities occur near the com-bustor wall at h > 20 mm. In these averaged imagesthe contribution from superequilibrium OH and “old”OH can hardly be distinguished. Only with the ad-ditional information from the deconvoluted chemilu-minescence images can it be stated that the high LIFintensities are well correlated with the flame zones.Noticeable phase-dependent differences are clearlyseen in the shapes of the irz (high OH LIF levels)and the inflow (very low LIF intensities). Around ph8,the inflow exhibits a curved shape (resembling bull-horns) with a bow around h = 30 mm. This bow isvery prominent at ph1 (at h ≈ 30 mm) and collapses

during the transition to ph2. The drastic change ofthe radial velocity component between h = 25 and35 mm at these phase angles also underlines the sig-nificant phase-dependent change of the flame at thislocation.

5.5. Correlation between temperature and mixturefraction at random phase

From the simultaneous measurement of the tem-perature and the species concentrations by laser Ra-man scattering, the correlations between differentquantities can be derived which contain the informa-tion about the thermochemical state of the flame. Thescatterplots in Fig. 13 show the correlation betweentemperature and mixture fraction for the quiet andpulsating flame, measured without phase correlation.Each symbol represents the result from a single-shotmeasurement recorded at various radial locations ath = 6 mm. The different colors help to identify dif-ferent radial regions of the flame. The solid line isthe result of a strained laminar flame calculation fora counterflow diffusion geometry with a strain rateof a = 1 s−1 [45,46], which represents a state closeto chemical equilibrium. The scatter in mixture frac-tion demonstrates that the premixing is not perfectand that there are variations between f ≈ 0.03 and0.07 for the quiet flame and between f ≈ 0.015 and0.08 for the pulsating flame (it should be kept in mindthat f is biased by about +7% for cold samples).

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Fig. 12. Phase-resolved averaged OH PLIF distributions at eight phase angles. Notice the slightly different color bar comparedto Fig. 11. Images are averaged over 200 single shots.

There are a lot of samples at room temperature thathave not reacted yet, mainly from the radial regionr ≈ 12–16 mm. In the inner recirculation zone thegas is close to equilibrium with high temperatures.The samples from the outer recirculation zone exhibitonly a low scatter in mixture fraction around fglob.

and their temperatures lie below the calculated curve.

This temperature reduction is probably due to heatloss to the burner plate. In addition the scatterplotscontain many samples with intermediate temperatures(i.e., between room temperature and flame tempera-ture). These partially reacted gas mixtures stem eitherfrom local flame extinction events or from the mix-ing of cold and hot gases that have not reacted yet

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Fig. 13. Correlation between temperature and mixture fraction for the quiet flame (left) and pulsating flame (right). Symbolsrepresent single-shot Raman measurements; the line shows a calculated curve for a near-equilibrium state. The global mixturefractions of the flames are indicated by the vertical lines; the stoichiometric mixture fraction is f = 0.055.

due to ignition delay [26]. Comparing the two scat-terplots, the major difference lies in the degree ofunmixedness of fuel and air. The phase-resolved Ra-man measurements will be considered further belowto determine whether the poorer mixing of the pulsat-ing flame stems from the thermoacoustic pulsations.

Fig. 14 illustrates the development of the scat-terplots for the two flames with increasing down-stream position. As expected, the mixing and reac-tion progress increases with downstream position, butpartially reacted mixtures are still present at h =30 mm. The reaction progress is slightly faster forthe quiet flame. This may be caused by the higherequivalence ratio of this flame and hence the highertemperature. Burnout is complete in the quiet flameat h ≈ 40 mm and in the pulsating flame at h ≈60 mm (not displayed). It is further seen that un-mixedness persists longer for the pulsating flame, sothat near-stoichiometric mixtures are still present ath = 30 mm. Finally, at h = 80 mm, mixing and re-action are complete and the thermochemical state ofthe flames is very close to equilibrium. The samplesdisplayed in the scatterplot of the quiet flame corre-spond to a standard deviation of the mixture fractionof 3.3% and of the temperature of 3.5%, which islargely caused by the inherent uncertainty of the mea-surement.

5.6. Mean temperature and mixture fractiondistributions at random phase

In order to compare the mean (Reynolds-averaged)mixture fraction distributions of the quiet and pulsat-ing flames, Fig. 15 displays 2D charts of f . Here, themean values measured at the different locations wereinterpolated using the program “Origin” to yield quasitwo-dimensional distributions. The scales for f arenot chosen to be identical because the global mixturefractions are not identical. However, both scales reach

from minimum to maximum f -values in each distri-bution. For the quiet flame the mean mixture frac-tion varies by �f = 0.0048 between fmean = 0.0465and fmean = 0.0513, and for the pulsating flame by�f = 0.0114 between fmean = 0.0361 and fmean =0.0475. This demonstrates again the different degreesof unmixedness of the two flames. In the quiet flame,high f -values are seen in the region of the inflow, andthe irz and orz are relatively lean. Here it must be con-sidered that according to the systematic measurementerror of approx. +7% for CH4 the evaluated mix-ture fraction is also biased to higher values, especiallyin low-temperature regions. With increasing tempera-ture the CH4 mole fraction and the bias of f decrease.In the pulsating flame, the mean f distribution revealsa separation of relatively rich and lean gases withinthe inflow with the lean gases appearing at the outerside of the inflow. In order to understand this behav-ior, the phase-dependent variations of f must be takeninto account. This will be done further below. For bothflames the measured f -values were slightly higherthan expected from the fuel and air flow rates. Forexample, at h = 60 mm in the quiet flame, the mea-surements resulted in an average value of f ≈ 0.0473in comparison to fglob. = 0.0463 and at h = 60 mmin the pulsating flame, the measured average wasf ≈ 0.041 in comparison to fglob. = 0.0391. Thisdeviation might be caused by an error of the flowme-ters, possibly together with a systematic deviationof the Raman measurement. One must also considerthat the cross section of the combustion chamber cov-ered by the Raman measurements (r = 0–30 mm) isonly 39% of the total cross section (85 × 85 mm), sothe average gas composition deduced from the Ra-man measurements does not necessarily reflect thevolume-averaged value.

The corresponding temperature distributions aredisplayed in Fig. 16. The lowest temperatures are,of course, measured in the inflow of the fresh gases

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Fig. 14. Scatterplots of temperature versus mixture fraction for the quiet and pulsating flames at h = 15, 30, and 80 mm.

and thus these distributions also visualize the aver-age shape of the inflow. It can be seen that the quietflame exhibits a larger opening angle than the pulsat-ing flame, consistent with the velocity distributionsshown in Fig. 5. The temperature level in the quietflame is, as expected, higher than that in the pulsat-ing flame, primarily due to the different equivalenceratios. The mean temperature gradients are steeper inthe quiet flame and this flame reaches a homogeneoustemperature distribution at lower heights than the pul-sating flame does. From the mean mixture fractionand temperature distributions one gets the impressionthat the structures in the pulsating flame are moresmeared out than in the quiet flame. This might beattributed to the periodic movement of the flowfield.

5.7. Correlation between temperature and mixturefraction at different phase angles

Fig. 17 displays T –f scatterplots at h = 6 mm.Again, each symbol represents the result of a single-shot measurement and the solid curve shows adia-batic equilibrium. Colors are used to distinguish be-tween different zones, i.e., the irz, the shear layerbetween the irz, and the inflow of fresh gases, theinlet flow, and the orz. Because these regions can-not be separated sharply, the colors serve more as aguide. It can be seen that the cyclic variations in theirz (r � 4–6 mm) and the orz (r � 16 mm) are rela-tively small and that these samples reflect reacted hotexhaust gas. Within the inflow and the neighboring

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Fig. 15. Distributions of mean mixture fraction (Reynolds-averaged) constructed from interpolations of the Raman point mea-surements. The results from the pulsating flame (right-hand side) have been recorded without phase triggering.

Fig. 16. Distributions of mean temperature constructed from interpolations of the Raman point measurements. The results fromthe pulsating flame (right-hand side) have been recorded without phase triggering.

shear layers, large changes of temperature and mix-ture fraction are observed. The majority of the sam-ples from this region have not reacted (T ≈ 300 K),a significant number have partially reacted, and somehave completely reacted. Astonishing are the largecyclic variation and the scatter of f , reaching fromf ≈ 0.015 (ph2–ph3) to f ≈ 0.1 (ph7–ph8). Theseresults indicate that the periodically changing pres-sure in the combustion chamber has different impactson the fuel and air supply lines in such a way thatmore fuel (or less air) enters the combustion chamberaround phases 7 and 8. The variations of f dimin-

ish with increasing height but are still observable ath = 35 mm.

5.8. Mean temperature and species distributions atdifferent phase-angles

The phase-dependent variations of the mean val-ues of f , T , and the mole fractions of CH4 and O2at h = 6 mm are displayed in Fig. 18. A striking fea-ture is the dramatic cyclic change of the mean mixturefraction within the inflow. From ph1 to ph6 the shapesof the radial profiles are quite similar, with a shallow

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Fig. 17. Phase-resolved scatterplots of temperature versus mixture fraction at h = 6 mm.

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Fig. 18. Radial profiles of the mean values (Reynolds averaged) of the mixture fraction, temperature, and mole fractions of CH4and O2 at h = 6 mm at different phase angles.

bump at r ≈ 5–10 mm and a dip at r ≈ 16 mm. At ph7and ph8, the profiles exhibit a completely differentshape, resembling a burst in comparison to the otherprofiles, and fmean exceeds even the stoichiometricmixture fraction (fstoich. = 0.055). The correspond-ing profiles of the CH4 mole fraction reveal that atthese phase angles high concentrations of CH4 are in-jected into the combustion chamber. The maximummean CH4 mole fraction, measured at r = 15 mm atph8, is 0.116 (taking into account the measurementbias of 7%, it would be 0.108). In comparison, atΦ = 0.7 the mole fraction of CH4 in the unburnedpremixed gas would be 0.0685. The lowest CH4 con-centrations were measured at ph4 and ph5, wheremaximum mole fractions were about 0.05. The pro-files of O2 are quite different from those of CH4: themaximum value of the profiles does not change muchwith phase angle and lies between 0.18 and 0.196.However, the width of the O2-profile changes signif-icantly during the oscillation cycle with a maximumaround ph7 and ph8 (halfwidth �r ≈ 9 mm) and aminimum around ph3 and ph4 (�r ≈ 4 mm). Theprofiles of f show a qualitative correspondence withthe CH4 profile but not with the O2 profile, so it canbe concluded that the mixture fraction is mainly influ-enced by the fuel flow variations. The corresponding

temperature profiles reveal large periodic variationsof T between r ≈ 7 mm and 15 mm. In the orz nochanges are observed and in the irz, for r � 5 mm,the changes are small. These profiles correspond wellwith the profiles of O2: at low temperatures the O2mole fractions are large and they decrease with in-creasing T , as expected.

5.9. Estimation of phase-dependent gas flow ratesinto the combustion chamber

From the results considered so far, it is clear thevelocities, temperature, and species concentrationsvary with phase angle. Now an estimation is pre-sented for the phase-dependent variations of the fueland air flows into the combustion chamber. Thereforethe molecular fluxes (number of molecules flowingthrough an area per time) of CH4 and O2 are consid-ered. The instantaneous molecular flux Si of a speciesi through the nozzle is the product u · ni integratedover the area of the nozzle, where ni is the mole-cular number density of the species i and u is theaxial velocity of the gas. These quantities change withtime and location and in order to determine Si , allquantities must be measured simultaneously over theentire area at h = 0. As this was not possible, the

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Fig. 19. Approximated molecular fluxes of CH4 and O2 into the combustion chamber and simplified pressure traces as a functionof phase angle.

following approximation was made: For each mea-suring location and phase angle, the mean values ofni (ni,mean) and u (umean) were used, with ni takenfrom the Raman measurements at h = 6 mm and u

from the LDV measurements at h = 5 mm. Cylindri-cal symmetry was also assumed for the flow. ThenSi,mean(r) was integrated over the area of the inflow(from r = 6 to 16 mm) for each phase angle by multi-plying ni(r) · u(r) at each measuring location r withthe area of an annulus around r with inner radius ri =r −1 mm and outer radius ro = r +1 mm. Finally, thetotal flux Si was determined by summing over all an-nuli. Of course, there are some crude simplificationsin this calculation that must be considered: (1) Theassumption of cylindrical symmetry of the flame wasconfirmed by taking images of the flame from vari-ous directions with respect to the square combustionchamber. The images did not reveal a difference inflame diameter, so that the assumption of cylindri-cal symmetry appears justified. (2) There were dif-ferences in height between the Raman measurements(h = 6 mm) and the LDV measurements (h = 5 mm).From the mean flow field it was estimated that theflow expands by less than 0.5 mm from h = 5 toh = 6 mm in the radial direction and that the changesin axial velocity are negligible. Therefore the errorfrom this approximation is also quite small. (3) Us-ing the mean values of n and u for the calculation ofS instead of the instantaneous ones is only correct if n

and u were statistically independent. This is certainlynot generally the case in this flame. However, withinthe inflow u is not expected to depend significantlyon gas composition, at least with respect to the ratioCH4/O2, which will be considered here. As an erroranalysis is unfeasible in this case, the results concern-ing the fluxes should be considered only an approxi-mation. With this in mind, some important trends can

be identified. The fluxes of O2 and CH4 calculatedin this way are shown in Fig. 19 together with simpli-fied pressure traces from the combustion chamber andthe plenum. It is clearly seen that the approximatedmolecular flux into the combustion chamber changessignificantly over an oscillation cycle and that CH4and O2 vary in phase with one another. Both reach apronounced maximum at phase 8 (315◦). The calcu-lated CH4 flux varies by a factor of 5.0 and the O2flux by 2.42. For comparison, the integrated chemi-luminescence intensity varied by a factor of 6.25.This is mentioned because there are grounds for sup-posing that the chemiluminescence intensity and thefuel supply rate are correlated. The pressures in theplenum and the combustion chamber are out of phaseby ≈80◦, as explained earlier, and it is clear that theaverage pressure in the plenum is higher than that inthe combustion chamber (by about 8 mbar). However,the traces shown in Fig. 19 and the displayed pres-sure difference (�p = pplenum −pcombustion chamber)are simplified in this graph. Comparing �p and thefluxes, it is seen that the maximum flux is reachedabout 100◦ after the maximum of �p. This value isclose to 90◦, which would be expected at the nozzleexit for a sinusoidal pressure variation in a configura-tion where only the pressure difference determines theinflow. The ratio (O2 flux/CH4 flux) is related to theequivalence ratio Φ and would be a direct measurefor Φ if no combustion occurred below h = 6 mm.For Φ = 0.7 the ratio would be 2.86, which occurs inFig. 19 around the phase angles 10◦ and 220◦. Thefact that the ratio changes between 1.84 (phase 8) and4.02 (phase 3) is evidence of a different response ofthe air and fuel supply lines to the pressure variationsin the combustion chamber and plenum. From the ob-served variation of the O2 flux it becomes apparentthat the air flow is subject to similar variations within

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the swirl generator and nozzle. If the CH4 injectionwithin the swirler varied with the same relative ampli-tude as the air flow, the measured ratio O2 flux/CH4flux would be constant over the period of oscilla-tion. This is inconsistent with the experimental result.However, considering that CH4 is injected with highmomentum into the air within the swirler, it can beassumed that the fuel line is less sensitive to the pres-sure variations than was the air supply. With this as-sumption, the qualitative explanation for the varyingequivalence ratio is as follows: When the flow veloc-ity of the air in the swirler is small due to a small �p

(around ph2), relatively large amounts of CH4 accu-mulate in the slowly flowing air. When �p rises, thisfuel-rich mixture is accelerated and enters the com-bustion chamber, leading to increased flow rates ofair and CH4 at h = 6 mm. This represents the firststep of the feedback loop known as oscillating fuelsupply combined with a convective time delay [29,47,48].

5.10. Distributions of f , CH4, and T at differentphase-angles

Fig. 20 shows the mixture fraction distribution forthe eight phase angles studied. Again, the mean valuesof f measured at the different locations were inter-polated using the program “Origin” to yield quasi-two-dimensional distributions. As the measurementswere performed at h = 6, 15, 25, 35, and 60 mm, theinterpolation is quite coarse in the upper part of theplots. It can be clearly seen that at ph7 and ph8 fuel-rich mixtures are injected and that these are convecteddownstream as the oscillation proceeds. Assuming anaverage axial velocity of u ≈ 30 m/s, the gas is con-vected about 104 mm during the oscillation period of3.45 ms, or 13 mm within 45◦. This is in qualitativeagreement with the observed development of the fuel-rich region between ph7 and ph2.

The next question to be addressed is where theCH4 is consumed. Fig. 21 displays the 2D distrib-utions of CH4 corresponding to the distributions off from the previous figure. The plot shows that theincrease of CH4 mole fraction near the nozzle be-gins at ph5 and continues until ph8. The CH4 plumealso increases in size, is convected downstream, andreaches its largest size around ph2. The region withr > 30 mm is not captured by the Raman measure-ments, but there are certainly significant CH4 con-centrations beyond this radial position. From ph2 on,the CH4 concentrations are drastically reduced, i.e.,CH4 is burnt. This observation is in good agreementwith the OH chemiluminescence measurement, whichexhibits a maximum around ph3. The correspondingpressure increase in the combustion chamber decel-erates the inflow into the combustion chamber and

Fig. 20. Interpolated 2D distributions of the mixture fractionfor eight phase angles from Raman measurements at h = 6,15, 25, 35, and 60 mm.

initiates the creation of the next fuel-rich gas pocketin the swirler.

The phase-dependent changes of the temperaturedistribution are displayed in Fig. 22. The temperature

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Fig. 21. Interpolated 2D distributions of the CH4 mole frac-tion for eight phase angles.

distribution is closely related to the CH4 distributionin such a way that high concentrations of CH4 cor-respond to low temperatures and vice versa, as ex-pected. The depletion of CH4 beginning at ph2 goesalong with an increase in temperature. The tempera-

Fig. 22. Interpolated 2D distributions of the temperature foreight phase angles.

ture distributions show further that the orz exhibits asignificant lower temperature than the irz for all phaseangles. With respect to the low temperatures reflect-ing the inflow, it is seen that this region undergoes asignificant change in shape from a cone with a rathersmall opening angle at ph1 to one with a large opening

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angle at ph6. From this movement it becomes clearthat the time-averaged temperature distribution fromFig. 16 appears smeared out in comparison to the non-pulsating flame.

5.11. The feedback loop of the self-sustainedpulsations

In the following, the sequence of events and thefeedback loop are briefly summarized, beginning withphase 3, where the integrated chemiluminescence in-tensity Ichem. (and probably also the heat release rate)is at a maximum. ph3: Ichem. and also the pressurein the combustion chamber are at a maximum. Theflow rate into the combustion chamber is low, andCH4 is accumulated in and slightly downstream ofthe swirler. ph4–ph5: Ichem. decreases together withpcomb. chamb.; the CH4 concentration in the combus-tion chamber drops because the inflow rate of CH4is still low. ph6–ph7: Ichem. and pcomb. chamb. ap-proach a minimum. CH4 is largely burnt in the regionof the main flame zone (h ≈ 40–60 mm). The pres-sure difference �p has become large, the flow ratesincrease, and a new CH4 plume appears at the nozzleexit. ph8: The flow rate into combustion chamber (ath = 6 mm) reaches a maximum. ph1–ph3: the CH4plume is convected to the main flame zone, leading toenhanced combustion; Ichem. and pcomb. chamb. in-crease.

Thus, an oscillating fuel supply is the source ofthe varying combustion intensity, which in turn trig-gers the pressure oscillation. The oscillating pressuregenerates a modulation of the fuel and air supplyrates in the swirler. This modulation of the CH4 flow(and equivalence ratio) is convected to the main flamezone. For an estimate of the convective time delay theresidence time of the gas in the nozzle, τnozzle, is ap-proximated using the flow rates and dimensions of thenozzle. The distance from the fuel injection withinthe swirler to the nozzle exit (h = 0) is about 4 cm.The mean cross section of the nozzle is approximately6.2 cm2. The flow rate of 612 slpm (see Table 1) cor-responds to 785 lpm at the measured nozzle exit tem-perature of T ≈ 350 K. This yields a mean velocity ofunozzle ≈ 21 m/s within the nozzle and a residencetime of τnozzle ≈ 1.9 ms. For the convection of thegas from h = 0 to the main flame zone at h ≈ 50 mma mean axial velocity of umean ≈ 30 m/s can be as-sumed (see Fig. 7), resulting in a time of flight ofτchamber ≈ 1.67 ms. The total convective time delayis thus estimated to be τ ≈ 3.57 ms. This is in goodagreement with the oscillation period of 3.45 ms andthus a further confirmation of the proposed feedbackmechanism.

6. Summary and conclusions

A gas turbine burner for premixed flames has beenequipped with an optical combustion chamber in or-der to perform investigations at atmospheric pressurewith optical and laser measuring techniques. Twoflames were studied, one with Φ = 0.7 exhibitingpronounced thermoacoustic pulsations at f ≈ 290 Hzand a second, quiet flame with Φ = 0.83. The mea-surements include pressure fluctuation registration,OH* chemiluminescence detection as an indicator forthe heat release rate, laser Doppler velocimetry, pla-nar laser-induced fluorescence of OH, and laser Ra-man scattering for the simultaneous detection of themajor species concentration and the temperature. Forcharacterization of the phase-dependent variations,phase-locked measurements were performed.

The flow field could be divided into three differ-ent regimes: the inflow of fresh gases and an innerand an outer recirculation zone. The flames were an-chored below the nozzle exit plane close to the irz,but the main flame zone appeared at h ≈ 40–60 mmand r � 20 mm. Although CH4 and air were pre-mixed in a manner typical of practical GT burners,a significant level of unmixedness was revealed bythe Raman measurements. These measurements alsoidentified pronounced effects of finite-rate chemistryin both flames.

Significant differences were observed betweenthe pulsating and quiet flames with respect to flameshape, flow field, mixing, and the reaction progress.In the pulsating flame, all measured quantities var-ied with the frequency of the pulsation. The totalOH* chemiluminescence intensity, which is, withincertain limits, representative of the heat release ratevaried between 16 and 100% over the oscillation cy-cle. These variations were in phase with the pressurevariation in the combustion chamber. The phase-dependent changes of the flow velocities were mostprominent near the nozzle. Here, the lower part ofthe irz moved up and down during an oscillation cy-cle, thereby changing the width of the inflowing gasstream. From the phase-resolved measurements ofmean axial velocity and the molecular number den-sities, the molecular fluxes within the inflow wereapproximated. The molecular fluxes of CH4 and O2varied in phase, but by different amounts, leading to aperiodic variation of the equivalence ratio. These vari-ations were in qualitative agreement with the pressurevariations in the plenum and combustion chamber.The convection of the mixtures with high or low CH4concentrations to the main flame zone triggered theheat release rate, which in turn caused the pressurevariations. The feedback loop for this flame is thusan oscillating fuel supply combined with a convectivetime delay. The reason for the oscillating fuel supply

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lies most probably in the different impedances of thefuel and air supply lines of the combustor. However,this was not explicitly determined in the investiga-tions.

The current work yielded phase-resolved quantita-tive data on the flow velocities, the major species con-centrations, mixture fraction, and temperature, whichare well suited for a comparison with results fromnumerical simulations. In the results presented here,mole fractions and time-averaged mean values wereused. However, the data archive also contains massfractions and Favre-averaged mean values. Finally, itshould be noted that the experimental data are avail-able on request for validation of numerical codes.

Acknowledgments

The work presented was mainly performed in theframe of the project “PRECCINSTA,” funded by theEuropean Union, and as part of the DLR project NA-COS. The financial support of these projects is grate-fully acknowledged. We furthermore thank C. Beratfor delivering the burner nozzle, B. Lehmann for theexecution of the LDV measurements, and M. Aigner,L. Hernandez and K. Syed for fruitful discussions.

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